Work, Energy and Power NCERT Solutions Class 11 Physics - Solved Exercise Question 6.15

Question 6.15:
A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m3 in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump?
Solution:
Volume of the tank, V = 30 m3
Time of operation, t = 15 min = 15 × 60 = 900 s
Height of the tank, h = 40 m
Efficiency of the pump, η = 30 %
Density of water, ρ = 103 kg/m3
Mass of water, m = ρV = 30 × 103 kg
Output power can be obtained as:
P0 = Work done / Time  = mgh / t
= 30 X 103 X 9.8 X 40 / 900  =  13.067 X 103 W
For input power Pi,, efficiency η, is given by the relation: 
η = P0 / Pi  =  30%
Pi = 13.067 X 100 X 103  / 30
= 0.436 X 105 W  =  43.6 kW

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